by **Armada** » Wed Nov 04, 2015 12:35 am

When I was learning proof by induction I also initially thought that this was a flaw in inductive reasoning, until I finally learned how to do proof by induction right. You can't give a proof by just showing that the base case and the next case holds. Besides the base case you also need to prove that if n holds, n + 1 also holds, for any n.

So to get a proof by induction that more beer always makes you feel better, you need to objectively prove that if I had n beers another beer (n + 1) will make me feel better. The mistake here is that this student thought that he had an inductive proof after showing he felt better after just two beers (base case + 1).

If only he had done his proof by induction right, he wouldn't need so many experiments. Unless of course the goal of his research was to get as drunk as possible.

When I was learning proof by induction I also initially thought that this was a flaw in inductive reasoning, until I finally learned how to do proof by induction right. You can't give a proof by just showing that the base case and the next case holds. Besides the base case you also need to prove that if [i]n[/i] holds, [i]n + 1[/i] also holds, [b]for any [i]n[/i][/b].

So to get a proof by induction that more beer always makes you feel better, you need to objectively prove that if I had [i]n[/i] beers another beer ([i]n + 1[/i]) will make me feel better. The mistake here is that this student thought that he had an inductive proof after showing he felt better after just two beers ([i]base case + 1[/i]).

If only he had done his proof by induction right, he wouldn't need so many experiments. Unless of course the goal of his research was to get as drunk as possible.